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A Central Limit Theorem For Mixing Triangular Arrays Of Variables Whose Dependence Is Allowed To Grow With The Sample Size

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  • Francq, Christian
  • Zakoïan, Jean-Michel

Abstract

Conditions ensuring a central limit theorem for strongly mixing triangular arrays are given. Larger samples can show longer range dependence than shorter samples. The result is obtained by constraining the rate growth of dependence as a function of the sample size, with the usual trade-off of memory and moment conditions. An application to heteroskedasticity and autocorrelation consistent estimators is proposed.

Suggested Citation

  • Francq, Christian & Zakoïan, Jean-Michel, 2005. "A Central Limit Theorem For Mixing Triangular Arrays Of Variables Whose Dependence Is Allowed To Grow With The Sample Size," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1165-1171, December.
    • Handle: RePEc:cup:etheor:v:21:y:2005:i:06:p:1165-1171_05
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    Cited by:

    1. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    2. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    3. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    4. Hafouta, Yeor, 2023. "Convergence rates in the functional CLT for α-mixing triangular arrays," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 242-290.
    5. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    6. Jacqueline C. Wisler, 2018. "U.S. CEOs of SBUs in Luxury Goods Organizations: A Mixed Methods Comparison of Ethical Decision-Making Profiles," Journal of Business Ethics, Springer, vol. 149(2), pages 443-518, May.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 114-144, January.
    8. Yaeji Lim & Hee-Seok Oh, 2016. "Composite Quantile Periodogram for Spectral Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 195-221, March.

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